There are four minutes to go in the period when one of the deans shows up at my door, just to give me a heads-up. I ask for a volunteer to finish the problem we just started. One of the seniors steps up, I toss him the marker and walk out into the hallway, confident that this will be worked out in detail by the time I get back.

From a hot-air-balloon 2 km high, the angles of depression to two towns in line with the balloon, are 81.2° and 13.5°. How far apart are the towns?

After my lovely conversation with the dean, I walk back in the room. Everyone is sitting at their desks. Looking at me. Then the board. Then at me. Uh-oh, they got stuck is what I’m thinking at this point. Then I look at the board.

The balloon caught on fire and crashed. So, this problem is now worthless.